Homotopy algorithm for structured matrix-variate Lasso and its application in online graph inference from matrix-variate time series.

par Yiye Jiang (Inria Grenoble)

lundi 26 janv. 2026, 14:00 → 16:00 Europe/Paris

In this talk, we propose a new autoregressive model for matrix variate time series, that is a sequence of matrices A(t) indexed by time. The model coefficient encodes a graph of the dependency structure among the entry time series A_ij(t). Motivated by the inference of the model coefficient, we extend the standard Lasso problem to a new type by assuming: 1. only a subset of parameters is sparse; 2. the parameters are constraint to follow a certain structure. The focus of the work is developing a new homotopy algorithm which allows to update a solution of the proposed Lasso optimization to the new solution when there is a new observation taken into account and/or the tuning hyperparameter is changed. The update avoids re-solving the whole problem, leading to computational advantages, on the other hand, it avoids storing all passed data. In the context of our statistical model, it allows the online fitting on the streaming data. We apply the methodology to analyze a real matrix-variate time series, where the matrix at each time records multiple weather measurements across locations. The inferred graphs from the model coefficient help to understand the dependency of weathers among locations.